This paper describes a simple and flexible new approach to rainfall-runoff transfer modeling, which jointly models the mean and the variance structure of runoff. Its mean is taken to be a linear autoregressive combination of present and previous rainfall and previous runoff, while its variance also depends on rainfall history. Inference for our model is performed using classical likelihood methods, and also by the more robust technique of quasi-likelihood, presupposing no particular distribution for runoff. The model has been developed on the Biorde catchment in Switzerland and calibrated and validated for 12 small Swiss catchments, with promising results. ¿ 2001 American Geophysical Union